Question

Найдите значение дроби...

Answer 1

$begin{array}{l}frac{x^2-5xy+y^2}{x+y+2}=frac{x^2-2xy+y^2-3xy}{x+y+2}=frac{(x-y)^2-3xy}{x+y+2}\frac{((3+sqrt5)-(3-sqrt5))^2-3xy}{(3+sqrt5)+(3-sqrt5)+2}=frac{(3+sqrt5-3+sqrt5)^2-3xy}{3+sqrt5+3-sqrt5+2}=frac{(2sqrt5)^2-3xy}{6+2}=\=frac{4times5-3times((3+sqrt5)(3-sqrt5))}8=frac{20-3times(3^2-(sqrt5)^2)}8=frac{20-3times4}8=frac88=1end{array}$